What is Contrastive Divergence

Contrastive Divergence is a popular algorithm in the field of unsupervised learning, a learning method in which the model learns from data without being explicitly told what to learn. The Contrastive Divergence algorithm was proposed by Geoffrey Hinton and his research team in 2002. Their ground-breaking paper described a method for training an energy-based model using gradient descent. This article will cover the following topics:
  • What is Contrastive Divergence?
  • How does Contrastive Divergence work?
  • Applications of Contrastive Divergence
  • Limitations of Contrastive Divergence
  • Conclusion
What is Contrastive Divergence?

Contrastive Divergence is a type of Markov chain Monte Carlo (MCMC) algorithm used for parameter estimation in probabilistic models. These models aim to estimate the probability distribution of a set of observed data given a set of parameters. Contrastive Divergence learns the parameters by sampling from the probability distribution and iteratively adjusting the parameters to fit the observed data. Contrastive Divergence is often used in Deep Learning and Neural Networks as a tool for unsupervised feature learning. Feature learning is the process of identifying and extracting features from raw data that can be used for a particular task. Unsupervised feature learning refers to the case where the features are learned automatically from data without the use of labels or supervision.

How does Contrastive Divergence work?
Contrastive Divergence was designed to address the high computational cost associated with training energy-based models such as Restricted Boltzmann Machines (RBMs). The traditional maximum likelihood estimation procedures require sampling from the model distribution many times to compute gradients, which is computationally expensive for large datasets. Contrastive Divergence works by exploiting a property of the probability distribution of the energy-based model, which allows samples from the model to be generated efficiently. These samples are then used to approximate the gradient of the log-likelihood function. The basic procedure for training an energy-based model using Contrastive Divergence is as follows:
  1. Initialize the model parameters
  2. Given an input data point, sample from the model to obtain a positive phase sample
  3. Starting with the positive phase sample, Gibbs sample k times to obtain a negative phase sample
  4. Update the model parameters using the difference between the positive and negative phase samples
  5. Repeat steps 2-4 until convergence is reached
The positive phase sample represents the probability distribution of the visible layer given the model parameters. The negative phase sample is obtained by sampling from the hidden layer given the visible layer, and then sampling from the visible layer given the hidden layer. The difference between the positive and negative phase samples is used to update the model parameters. The Gibbs sampling procedure is used to generate the negative phase sample. Gibbs sampling is a Markov chain Monte Carlo method for simulating samples from a probability distribution. The procedure involves initializing a state of the chain (in this case, the visible layer), and iteratively sampling from the conditional probability distribution of each variable given the current state of the chain. The final state of the chain is then used as the sample.

Applications of Contrastive Divergence
Contrastive Divergence is a useful algorithm in many areas of machine learning, including:
1. Reinforcement Learning: In reinforcement learning, the agent learns to perform a task through trial and error, using feedback from the environment to adjust its behavior. Contrastive Divergence can be used to learn a policy for an agent, allowing it to make decisions based on the state of the environment.
2. Anomaly Detection: Anomaly detection involves identifying outliers in a dataset that deviate significantly from the norm. Contrastive Divergence can be used to learn a probability distribution of the normal data, allowing anomalies to be identified as data points with low probability.
3. Collaborative Filtering: Collaborative filtering is a technique used in recommender systems to suggest items to users based on the interests of similar users. Contrastive Divergence can be used to learn a model of user-item interactions, allowing accurate recommendations to be made.

Limitations of Contrastive Divergence
While Contrastive Divergence is a useful algorithm, it has some limitations:
1. Inability to optimize the partition function: The partition function is a normalization constant that ensures the probabilities sum to one. It is notoriously difficult to compute for energy-based models, and Contrastive Divergence does not optimize it. This can lead to problems in models with many hidden units.
2. Lack of solid theoretical grounding: The theory behind Contrastive Divergence is still not well understood. While it has been shown to work well in practice, there is no clear theoretical justification for why it works.
3. Sensitivity to the number of Gibbs steps: The number of Gibbs steps used in Contrastive Divergence can significantly affect the performance of the algorithm. Too few Gibbs steps can lead to bias in the estimates, while too many can lead to high variance.

Contrastive Divergence is a powerful algorithm in the field of unsupervised learning, with applications in several domains. Its ability to learn features automatically from data has made it a popular technique in Deep Learning and Neural Networks. However, it does have some limitations, including the lack of theoretical grounding and the sensitivity to the number of Gibbs steps used in the algorithm. Overall, Contrastive Divergence is a useful tool for researchers and practitioners in the field of machine learning.